eflowRecursiveGaussLegendreIntegrator< IntegrandType > Class Template Reference

Class to perform a generic recursive Gauss-Legendre Integration, see http://en.wikipedia.org/wiki/Gaussian_quadrature#Gauss.E2.80.93Legendre_quadrature Templated in the type of the integrand. More...

#include <eflowCellIntegrator.h>

Collaboration diagram for eflowRecursiveGaussLegendreIntegrator< IntegrandType >:

Public Member Functions
	eflowRecursiveGaussLegendreIntegrator (IntegrandType *integrand, double error)
virtual	~eflowRecursiveGaussLegendreIntegrator ()
virtual double	integrate (const eflowRange &range)
double	getError () const

Private Member Functions
double	DoGaussLegendreIntegration (const eflowRange &range, int nOrder)
double	RecurseIntegration (const eflowRange &range, int nSubRanges)

Private Attributes
IntegrandType *	m_integrand
double	m_error
int	m_depth

Detailed Description

template<class IntegrandType>
class eflowRecursiveGaussLegendreIntegrator< IntegrandType >

Class to perform a generic recursive Gauss-Legendre Integration, see http://en.wikipedia.org/wiki/Gaussian_quadrature#Gauss.E2.80.93Legendre_quadrature Templated in the type of the integrand.

All the integrand class needs to have, is an evaluate() method, that takes a double as a parameter and returns a double. Templates are used instead of polymorphism here due to the better CPU performance.

Definition at line 34 of file eflowCellIntegrator.h.

Constructor & Destructor Documentation

eflowRecursiveGaussLegendreIntegrator()

template<class IntegrandType>

eflowRecursiveGaussLegendreIntegrator< IntegrandType >::eflowRecursiveGaussLegendreIntegrator ( IntegrandType * integrand, double error )

inline

Definition at line 36 of file eflowCellIntegrator.h.

                                                                                :
    m_integrand(integrand), m_error(error), m_depth(1) {
    assert(m_integrand);
  }

~eflowRecursiveGaussLegendreIntegrator()

template<class IntegrandType>

virtual eflowRecursiveGaussLegendreIntegrator< IntegrandType >::~eflowRecursiveGaussLegendreIntegrator ( )

inlinevirtual

Definition at line 40 of file eflowCellIntegrator.h.

{ }

Member Function Documentation

DoGaussLegendreIntegration()

template<class IntegrandType>

double eflowRecursiveGaussLegendreIntegrator< IntegrandType >::DoGaussLegendreIntegration ( const eflowRange & range, int nOrder )

inlineprivate

Definition at line 61 of file eflowCellIntegrator.h.

                                                                        {
    /* Perform nth order Gauss-Legendre quadrature, see
     * http://en.wikipedia.org/wiki/Gaussian_quadrature#Gauss.E2.80.93Legendre_quadrature */
 
    /* Array offset for legendre weights/roots */
    int j = nOrder * (nOrder - 1) / 2;
    const double* roots   = legendreRoots   + j;
    const double* weights = legendreWeights + j;
 
    double rangeCenter    = range.getCenter();
    double rangeHalfWidth = range.getWidth()/2;
 
    double I = 0.0;
    double x;
    if(m_integrand){
      for (int i = 0; i < nOrder; i++) {
    x = rangeCenter + roots[i] * rangeHalfWidth;
    I += weights[i] * m_integrand->evaluate(x);
      }
    }
    else{
      std::cerr << "eflowCellIntergrator::DoGaussLegendreIntegration ERROR : Invalid pointer to IntegrandType and cannot perform integration" << std::endl;
    }
    if (I < 0. || rangeHalfWidth < 0.) std::cerr << "eflowCellIntergrator::DoGaussLegendreIntegration WARNING: I = " << I << "\trange = " << range.print() << std::endl;
 
    return I * rangeHalfWidth;
  }

getError()

template<class IntegrandType>

double eflowRecursiveGaussLegendreIntegrator< IntegrandType >::getError ( ) const

inline

Definition at line 57 of file eflowCellIntegrator.h.

{return m_error;}

integrate()

template<class IntegrandType>

virtual double eflowRecursiveGaussLegendreIntegrator< IntegrandType >::integrate ( const eflowRange & range )

inlinevirtual

Definition at line 42 of file eflowCellIntegrator.h.

                                                    {
    /* Try a 5th and 6th order Gauss-Legendre quadrature */
    double I5 = DoGaussLegendreIntegration(range, 5);
    double I6 = DoGaussLegendreIntegration(range, 6);
 
    /* If results agree within m_error threshold, return the mean... */
    double Imean = (I5 + I6) / 2.0;
    if (fabs(I5 - I6) / Imean <= m_error) {
      return Imean;
    } else {
      /* ...else recursively part up the integration into n subRanges */
      return RecurseIntegration(range, 2);
    }
  }

RecurseIntegration()

template<class IntegrandType>

double eflowRecursiveGaussLegendreIntegrator< IntegrandType >::RecurseIntegration ( const eflowRange & range, int nSubRanges )

inlineprivate

Definition at line 89 of file eflowCellIntegrator.h.

                                                                    {
    m_depth++;
    /* Part up integration range in n subRanges */
    double subRangeWidth = range.getWidth() / nSubRanges;
    eflowRange subRange(range.getMin(), range.getMin() + subRangeWidth);
 
    /* Loop over subranges */
    double Integral(0.0);
    for (int i = 0; i < nSubRanges; i++) {
      Integral += integrate(subRange);
      subRange.shift(subRangeWidth);
    }
    m_depth--;
 
    return Integral;
  }

Member Data Documentation

m_depth

template<class IntegrandType>

int eflowRecursiveGaussLegendreIntegrator< IntegrandType >::m_depth

private

Definition at line 108 of file eflowCellIntegrator.h.

m_error

template<class IntegrandType>

double eflowRecursiveGaussLegendreIntegrator< IntegrandType >::m_error

private

Definition at line 107 of file eflowCellIntegrator.h.

m_integrand

template<class IntegrandType>

IntegrandType* eflowRecursiveGaussLegendreIntegrator< IntegrandType >::m_integrand

private

Definition at line 106 of file eflowCellIntegrator.h.

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The documentation for this class was generated from the following file:

• eflowCellIntegrator.h